In a statement posted on the golfer's Web site, the family said it will continue to provide updates about any change in Ballesteros' condition.
The statement added that the family "takes this opportunity of thanking everyone for the support that both Seve and his own family have been receiving during all this time."
Ballesteros, now 54, was diagnosed with two malignant brain tumors in October 2008 after he lost consciousness twice - at the Madrid international airport and at a restaurant in the Spanish capital.
The golfer was hospitalized for 72 days at Madrid's Hospital de La Paz and underwent four life-threatening operations to remove the tumors and reduce swelling inside his skull.
Ballesteros later went through several cycles of chemotherapy and radiotherapy and also had to relearn basic motor skills that had been lost following the operations.
He also suffered loss of sight in his left eye and speech impairment.
The golfer has spent his convalescence in his hometown of Pedreña, in northern Spain, but returned to Madrid on June 2009 to launch the Severiano Ballesteros Foundation, whose main purpose is to finance and promote brain cancer research.
Rumors began surfacing in Spain last week that Ballesteros' health had taken a turn for the worse.
The family told Efe that Ballesteros is currently sedated and his vital signs are being monitored constantly.
Ballesteros is a former world No. 1 who holds the record for most European Tour titles (50) and was elected to the World Golf Hall of Fame in 1999.
He captured six Major championships during his career: four British Opens - in 1979, 1984 and 1988 - and two Masters - in 1980 and 1983.